“FUN” PROBLEM #4
1. Find a number which is 10 more than its additive inverse.
Number = x x= -x + 10 the number is 5
Additive Inverse = -x 2x = 10
x = 5
2. Find a number which is 14 less than its additive inverse.
Number = x x= -x - 14 the number is -7
Additive Inverse = -x 2x = -14
x = -7
3. Seven times a certain number is nine less than twice number. Find the number.
Number = x 7x = 2x - 9 the number is -9/5
5x = -9
x = -9/5
4. Seven times a certain number is fourteen more than five times the number.
Number = x 7x = 5x +14 the number is 7
2x =14
x = 7
5. Frank challenged: “Six years ago I was half as old as I am old. How old am I?”
Frank present = x x-6 = 1/2 x 12
Six years ago = x-6 -6 = -1/2 x
12 = x
6. Ada declared, “Twenty years from now I will be three times as old as I am now. How old am I?”
Present = x x +20 = 3x 10
Future = x + 20 20 = 2x
10 = x
7. Roger had 6 steel balls of the same size and shape. He found that when he put 5 of the balls in one pan of a beam balance and put the sixth ball and a 100-gram weight in the other pan, the pans were in balance. How much did each ball weigh?
Weight of 1 ball = x 5x = x+100 25
4x = 100
x = 25
8. Wilma has six coins of the same kind. A dollar and two of the coins have the same total value as all six coins put together, what kind of coin does Wilma have?
Value of 1 coin = x 100 + 2x = 6x 25 cents
100 = 4x
25 = x
9. A mother aged 29 has a 5-year old daughter. In how many years will the mother be four times as old as her daughter?
How many years future = x 29 + x = 4(5+x) 3
Mother future= 29+x 29 + x = 20+4x
Daughter = 5+x 9 = 3x
3 = x
10. Fifteen old Al has an uncle who is 43 years old. How many years ago was the uncle fives times as old as Al was?
Years past = x 43-x = 5(15-x) 8
Al = 15-x 43-x = 75-5x
Uncle = 43-x 4x = 32
x = 8